What exactly is the difference between these two phrases. How does けど/が affect the meaning and how does it relate to its meaning of 'but'?
The difference between the two is the percentage of conviction in what you are saying.
Ending sentences with です usually indicates 100% of conviction.
On the other hand, sentences ending in といいんですけど would be lower than 100%.
Though the two phrases would mean the same thing, the nuance is slightly different.
Note: Sometimes ですけど can just be used as a conjunction while speaking, without any nuance of "but". It really depends on the entire context of the conversation.